X-ray imaging: Fundamentals and planar imaging

Transcription

1 X-ray imaging: Fundamentals and planar imaging By Mikael Jensen and Jens E. Wilhjelm Risø National laboratory Ørsted DTU (Ver /12/07) by M. Jensen and J. E. Wilhjelm 1 Overview X-ray imaging is the most widespread and well-known medical imaging technique. It dates back to the discovery by Wilhelm Conrad Röntgen in 1895 of a new kind of penetrating radiation coming from an evacuated glass bulb with positive and negative electrodes. Today, this radiation is known as short wavelength electromagnetic waves being called X-rays in the English speaking countries, but Roengten rays in many other countries. The X-rays are generated in a special vacuum tube: the X- ray tube, which will be the subject of the first subsection. The emanating X-rays can be used to cast shadows on photographic films or radiation sensitive plates for direct evaluation (the technique of planar X-ray imaging) or the rays can be used to form a series of electronically collected projections, which are later reconstructed to yield a 2D map (thus, a tomographic image). This is the so-called CAT or CT technique (see the chapter on CT imaging). 1.1 Characterization of X-ray X-rays are electromagnetic radiation (photons) with wavelengths, 10 pm < λ < 10 nm. They travel with the speed of light, c km/s and has a frequency of ν = c 0 /λ [Hz]. The energy of the individual photon is E = hν [J], where h = Js is Planck s constant. The energy of an X-ray is typically measured in electron volts (ev). 1 ev is the energy increase that an electron experiences, when accelerated over a potential difference of 1 V. Thus, 1 ev = q e ΔV = J, where the charge of an electron is q e (both q e and ΔV is negative in this context). Problem: Calculate the frequency and energy for monochromatic x-rays with λ = 1 nm. Answer: ν = c 0 /λ Hz = THz. E = hν J = 1.24 kev. Protective lead Cathode (heated filament) Glass envelope I Electrons Anode + U X-rays Figure 1 X-ray tube showing cathode and anode with electrons accelerated from cathode towards anode. The tube generates X-rays in all directions, but due to the encapsulation most are lost and only a fraction is used for imaging. 1/8

2 Characteristic X-ray emission from Wolfram 1200 Relative intensity at fixed electron current mm Al filter cut-off V=50kV V=90kV V=140kV Photon energy (kev) Figure 2 X-ray emission from Wolfram anaode X-ray tube. Observe that for a given tube voltage, the higher the energy of the photons, the less there are. And if the number of photons are to increase, then the tube voltage should increase. Data from [1]. 1.2 X-ray generation: The X-ray tube A typical X-ray tube is depicted in Figure 1. It consists of an evacuated glass bulb with a heated filaments (glødetråd in Danish) as the negative electrode and a heavy metal positive anode. Thermic electrons emitted by the heated filament are accelerated across the gab to the anode. If the voltage be- Figure 3 Rotating anode X-ray tube. "RTM" anode designates a Molybdenum anode mixed with 5% Rhenium to improve the thermal stability. The metal anode is supported by graphite to improve the total thermal capacity. Source: Siemens. 2/8

3 tween cathode and anode is U volts and the current in the tube being I amperes, each electron will be hitting the anode with a kinetic energy of U ev. The power deposited in the anode will be I times U, and the total energy transferred to the anode in an exposure lasting t seconds will be IUt. The electrons will be slowed down in the anode material, mainly releasing their energy as heat, but to a small degree (few percent) the energy is transformed to either Bremsstrahlung or characteristic X-rays. The Bremsstrahlung originates from the sudden deacceleration and direction changes of the primary electrons in the field of the anode atoms, the characteristics X-rays originates from the knockout and subsequent level filling of inner electrons in the atoms of the anode material. The highest possible quantum energy of emanating X-rays (measured in ev) will be equal to U. Typical energy spectra as a function of voltages are shown in Figure 2. Please note that the spectra are all taken at the same current, only the voltage has been varied. This demonstrates that the total number of X-ray photons are heavily dependent on tube voltage. In addition to the information in Figure 2, a general rule of thumb says that 15 kev increase in voltage corresponds to a doubling of the photon output. For practical medical applications, the low energy part of the photons are normally not used but removed by filtering either inside or just outside the X-ray tube. Normal filter materials are either aluminium or copper. The thicker the filter and the higher the atomic number of the filter, the greater the cut-off of low energy photons. The description of the exposure characteristics of a given X-ray tube will comprise the voltage (in units of kv), the current (in units of ma), the time of exposure (in units of s) and the degree of filtering (for example a plate of Al, one mm thick next to a plate of Cu, 0.5 mm thick). As the total number of photons produced for a given high voltage setting only depends on the product of current and time this is often stated as a product in units of mas. Protective shield of lead X-ray tube Al-filter (removes low energy radiation) Collimator Object Secondary radiation (Compton scattering) Film Grid Screens Figure 4 Schematic illustration of a typical X-ray system. 3/8

4 focus FFD FOD object film Figure 5 Definition of distances corresponding to Figure 4. FOD = focus to object distance. FFD = focus to film distance. 1.3 Anode material, power dissipation Heavy elements are normally preferred for anode materials as the high Z-number gives efficient production of the part of the X-ray that originates from Bremsstrahlung. The characteristic X-ray lines, which add to the total energy spectrum, normally lies in the middle of the medical useful energy range (50-70 kev). The thermal load on the anode material both during the short exposures and averaged over time when performing rapid, multiple exposures heats the anode dramatically. For this reason, normally a high melting point material is used. Anodes made out of Tungsten (W) are very common. The area of thermal dissipation can be enlarged by rotating the anode during exposure. An example of such a device is shown in Figure 3. 2 Typical X-ray system Figure 4 shows a typical X-ray system. The X-ray is generated by the X-ray tube (Røntgenrør). Low energy photons are removed by the Al filter, since as they cannot penetrate the object and contribution to the information on the film, they would only add needless to the dose received by the object. X-ray radiation outside the image region on the film is removed by the collimator (primærblænde). Attenuation (what is measured on the film) and Compton scattering take place at the object. Only photons moving directly from the source to the film are allowed through the grid at the bottom (sekundærblænde). 4/8

5 3 Geometrical considerations Referring to Figure 5 we can define the distance from the X-ray origin (the focus 1 ) to the objects as FOD. The distance from the focus to the film 2 or any other medium of radiation detection can be defined as FFD. Any object will to some degree attenuate the X-ray, and variation in X-ray absorption across the objects will create a corresponding variation in the radiation impinging on the film. An unavoidable and sometimes desirable geometrical magnification of the image relative to the object can be deduced from the triangle in Figure 5. The enlargement factor F, can be defined as: 3 F = size of film image / size of object = FFD / FOD (1) If near to normal picture size and little variation in enlargement is sought for organs having different depths in the body, the geometrical magnification should be minimized by using a large focus to film distance (FFD) and a small object to film distance. A small object to film distance also improves image contrast, as blurring by scattering increases with increasing distance between object and film. This is because the origin of the scatter is mainly inside the object: The longer the scattered radiation is allowed to travel between the object and the film, the more this radiation diverges from the true unscattered photons. Similar geometrical considerations (i.e. similar triangles) can demonstrate that extended size of the focus will generate blurring on the film. 4 Origins of contrast in the X-ray image X-rays are attenuated according to the normal linear attenuation law: I(x) = I 0 exp(-μx) = I 0 exp(-μ/ρ xρ) (2) where x is the distance transversed in the material and μ is the so-called linear attenuation coefficient in units of m -1. I 0 is the intensity at the entrance to the material (x = 0) and I(x) is the intensity at distance x. In the latter part of (2), ρ is the density of the material. By giving the attenuation coefficient in units of μ/ρ and the thickness in length times density (area weigth, e.g. g/cm 2 ) the attenuation coefficient (now called mass attenuation coefficient) becomes independent on the physical state of the material. Mass attenuation coefficients for some common tissues are given in Table 1. The microscopic description of the attenuation comprises photo electric effects and Compton scattering, which are both described in the chapter on nuclear medicine. For the understanding of the X-ray technique, it suffices to say that the linear attenuation coefficient for human tissues varies approximately as the electron density. Thus, it varies roughly proportional with the physical density (kg/m 3 ). Air has the lowest density, lung tissue has lower density than fat, fat has lower density than muscle, again having much lower density than the bone mineral of the skeleton. The X-ray attenuation varies accordingly. X-rays transversing parts of the body having high absorbing material will be much more attenuated, and the film or radiation capture device will in this region not receive as much radiation. 1. The "focus" is in this context the source of the X-ray photons, as it is the name for the electron spot on the anode of the X-ray tube. 2. The term "film" is still common language, even though the conventional x-ray film to a large degree has been replaced by various other imaging plates. 3. Here size means any distance e.g. the length of a given object. 5/8

6 It should be remembered that the X-ray image is a negative (bright areas correspond to high attenuation) and that the image is a 2D projection of the 3D distribution of attenuation. Table 1: Mass attenuation coefficients for typical tissues in μ/ρ. From [2]. µ ρ given in cm 2 /g 50 kev 100 kev 200 kev Air ρ=0,0013 g/cm 3 0,208 0,154 0,122 Water ρ=1,00 g/cm 3 0,227 0,171 0,137 Adipose tissue ρ=0,95 g/cm 3 0,212 0,169 0,136 Muscle ρ=1,05 g/cm 3 0,226 0,169 0,136 Bone ρ=1,92 g/cm 3 0,424 0,186 0,131 Lead ρ=11,35 g/cm 3 8,041 5,549 0,999 An example of a normal X-ray image of the chest (one of the most common medical imaging procedures) is seen in Figure 6. Notes that the most attenuating areas (ribs, vertebral column, heart) appear white while the lungs with little attenuation appear black. The image information in the planar X-ray is mainly anatomical, actual densitometric measurements on the film are only performed for quality assurance programs and yields little medical information. Today, all planar X-ray images are evaluated by a human observer. Trachea Clivacula Lung field Lung field Aortic arc Left Ventricle of Heart Liver Diaphragma Figure 6 Normal chest X-ray image. This image is recorded with a tube voltage of 150 kv to minimize the contribution from bone. 6/8

7 5 Film, intensifyer foils and screens Originally, the radiation was captured by a normal photographic film. In the film, the energetic X- ray photons are absorbed in the silver halide (NaB-NaI) crystals, generating very small amounts of free silver. During film processing, any grain with small amounts of free silver are completely converted to metallic, nontransparent silver, while the remaining unreduced silver halide is removed by the fixative. X-ray films are of course made to the size necessary for the anatomical situation in question and can be very large. To increase sensitivity and thus lower radiation dose, the photo sensitive film emulsions are often thicker and occasionally coated on both sides of the film, in contrast to normal photographic film. The silver contents of the films makes X-ray films rather expensive. Any film has a specific range of optimal sensitivity (exposure range from complete transparency to completely blackened). Although modern equipment are normally assisted by electronic exposure meters, the correct choice of film, exposure time, exposure current and high voltage is still left to the judgement of the X-ray technician. To improve the sensitivity and thus lower radiation exposure to the patient, the film is often brought in contact with a sheet of intensifying screen. The screen contains special chemical compounds of the rare earth elements, that emits visible blue-green light when hit by X-rays or other ionizing radiation. This permits the use photographic film with thinner emulsions and more normal sensitivity to visible light. While increasing the sensitivity, the use of intensifying screen on the other hand blurs the images as the registration of X-ray radiation is no longer a direct, but an indicted process. The patients or the object is not only the source of X-ray absorption but also of X-ray scattering, mainly due to Compton effect (please see the chapter on Nuclear Medicine). Any part of the patient exposed to the primary X-ray beam will be a source of secondary, scattered, X-rays. These X-rays will have lower energy than the original ray, but as no energy discrimination is used in the registration, also the secondary scattered radiation adds to the blackening of the film. The scattered radiation carries no direct geometrical information about the object and thus only reduces the contrast by increasing the background gray level of the film. Scattered radiation can to some degree be avoided by the use of special collimators called raster. The raster can be a series of thin, closely lying bars of lead, only allowing radiation coming from the direction of the focus point to hit the film while other directions are excluded. A typical example of a complete radiography cassette content is shown in Figure 7. 6 Digital radiography and direct capture During the last years the conventional film based radiography has gradually been replaced by newer digital techniques. The end points is of course the acquisition and storage of the X-ray image information as computer files. It should be noted that X-ray images are normally of very high resolution (more than four thousand by four thousand pixels) with large dynamic range (12 to 16 bits). The correct handling and display of such image information without loss or compression is still the subjects of specialized workstations. The digital X-ray images are normally stored and displayed in so-called PACS systems (Picture Archiving and Communications System). The image information is either temporarily captured on phosphor plates for subsequent transfer to digital storage by so-called phosphor plate readers, in function much related to the old X-ray film processors) or by direct, position sensitive electronic X-ray detection devices, the so-called direct capture systems. At present (2003) the geometrical resolution of the various digital techniques is still somewhat inferior to the best possible film technique. However, the benefits of rapid viewing, interactive image availability, postprocessing and digital transmission often outweighs the reduction in image quality. For special 7/8

8 applications, like breast cancer detection by mammography, the photographic film is still the system of choice. X-ray passing through the raster X-ray not passing through the raster c f r Figure 7 X ray cassette, containing double coated film (f), intensifying screen (c) and raster (r). 7 References [1]Johannes Jensen og Jens Munk: Lærebog i Røntgenfysik, Odense udg. s.121. [2]Data from 8/8

9 1 Overview CT scanning By Mikael Jensen & Jens E. Wilhjelm Risø National laboratory Ørsted DTU (Ver /9/07) by M. Jensen and J. E. Wilhjelm) As it can be imagined, planar X-ray imaging has an inherent limitation in resolving overlying structures as everything seen in the images are the result of a projection. It is, however, possible to resolve the 3D distribution of X-ray attenuation from a set of projections. This is actually what we do mentally when we access the 3D structure of an object, for example the head of a person, by walking around the object and looking at it from all different angles. The CT scan is exactly such a reconstruction of the 3D distribution based on a large set of X-ray projections obtained at many angles covering a complete circle around the patient. CT is an abbreviation of computed tomography. In Anglo-American literature one also occasionally finds the abbreviation CAT denoting computed axial tomography. Tomography by itself means the rendering of slices: naturally the 3D information cannot easily be displayed 3 dimensionally on a screen, instead it is most often displayed as a series of axial slices. The CT scanner was developed in the early 1970ies by Geoffrey Hounsfield and and his colleague Alan Cormack in England (actually working for EMI on funds stemming from music record sales). For this they were awarded the Nobel Prize in Medicine in The basic three components of a CT scanner are still the same as in planar X-ray imaging: An X-ray tube, an object (patient) and a detection system. In the earliest scanners the output of the X-ray tube was collimated to a narrow, pencil-like beam and detected by a single detector. X-ray tube and detector were translated in unison (see Figure 1) across the object making a linear scan. After each scan, Figure 1 Early CT scanner geometry 1/8

10 Rotating X-ray tube Rotating X-ray tube Patient Patient Static ring of detectors Rotating arc of detectors Active detectors Figure 2 Geometry of gantry in CT scanner. Left: The third generation is of type rotate-rotate, where both X-ray tube and detectors rotate. Right: The fourth generation is of type rotate-fixed, where only the X-ray tube rotate. The x-ray tube emits a fan-shaped beam. typically lasting 10 seconds, the entire setup was rotated a few degrees, the scan repeated, and so forth. From a set of such 256 scans the final image (a single slice) would be reconstructed by overnight computing. This reconstruction - which derives an image from a large set of projections - will be considered in Subsection 2.3. Modern scanners are now essentially of two types: the rotate-rotate system and the rotate-fixed system. These are illustrated in Figure 2. Both systems use narrow fan-shaped beams collimated to spread across the full width of the patient. In the rotate-rotate system as many as 700 detectors may be placed in an arc centered at the focal spot of the X-ray tube. The tube is run continuously as both it and the detectors revolve around the patient. The fast electronics of the detectors take as many as thousand readings per detector for a total of readings in one second. In the rotatefixed system as many as 2000 fixed detectors form a circle completely around the patient. The X-ray tube is rotating concentrically within the detector ring. The detectors are normally focused at the centre of the ring. Acquiring the detector responses every one third of a degree produces more than readings per second. 1.1 Hounsfield value Using mathematical algorithms (as will be shown latere in Subsection 2.3), the computer can calculate the linear attenuation coefficient for each point (pixel) in the object and assign an attenuation value to it. Normally, this attenuation is not depicted as attenuation coefficients, instead radiology uses a special unit, now called Hounsfield unit (HU). The corresponding Hounsfield value is defined as follows: HV = 1000 (μ m -μ w )/ μ w (1) where μ m is the (average) linear attenuation coefficient within the voxel it represents and μ w is the linear attenuation coefficient for water at the same spectrum of photon energies. The Hounsfield unit is dimensionless. From the above definition, one should think, that the Houndsfield values are very well-defined. This is not so, as can be seen from Figure 3, which represent data from two different teaching books. There can be a number of reasons for these differences: Different spectra of emitted energy (the center frequency (or energy) of the spectrum, the shape of the spectrum). 2/8

11 (a) (b) Figure 3 Hounsfield values according to different text books: (a) is from [2] while (b) is from [3]. As can be seen, the values does not fully agree. Different definitions of what a given tissue type actually represents. Tissue types seldomly consist of just one component (e.g. muscular tissue can contain various amount of lipid, but still be described as muscular tissue ). 1.2 Single slice versus multi-slice system Originally the CT scanner only acquired one slice at a time, making extended axial field of view a time consuming process. Today the scanners, whether of the third or fourth generation, acquire many slices (16 to 256) at a time using an X-ray tube with an extended axial beam and multiple stacked detector chains. Rotation time is now down to fractions of a seconds making acquisition of of multi-slice 3/8

12 representation of the heart, almost motion arrested. If the patient is continuously slid through the gantry ring during the rotation, a so-called spiral CT scan is acquired. Proper reconstruction can thus yield large series of closely lying slices over extended parts of the body, in principle from head to foot. 2 System details 2.1 CT scanner X-ray tube Proper reconstruction of the CT scans is only possible if a very large number of photons are available for the detectors. If the acquired projections are not statistically well-determined, the reading from a detector will be noisy and the reconstruction algorithm will propagate this noise, leading to unacceptable high noise in the final image. Thus, normally, the CT scan is done with a high output from the CT tube corresponding to large kilovolts and milliampere settings. As the scan are normally extended for many slices and many revolutions, the final dose can be as high as 50 to 100 millisievert (see definition of Sievert in nuclear medicine chapter of this book). As the number of CT scans has been increasing with the wide spread installation of potent multi-slice and/or spiral scanners, the total collective radiation dose from CT scans to the entire medical irradiation constitutes a major part The high current and voltage and the extended exposure time, deposits very large amounts of primary electron beam energy in the anode of the X-ray tube. Special tubes have been developed for these X-ray scanners, with large, fast rotating anodes of high melting point materials. Special problems are related to the technology of bringing electricity of high voltage forward to the X-ray tube, rotating at an orbital diameter of more than one meter with the speed of more than two revolutions per minute. The rapid revolution of X-ray tube and perhaps detector chain also puts a large mechanical strain on the entire X-ray gantry, which must be of extraordinary sturdy construction. 2.2 Detector chain technology Today, at least three types of detectors are used. These detectors can be classified according to the type of material stopping the X-rays: Gas (Xenon) I0 I0 I0 μ11 μ12 Ir1 = I0 exp(-μ11dx -μ12dx) I0 μ21 μ22 Ir2= I0 exp(-μ21dx -μ22dx) Ic2 = I0 exp(-μ12dx -μ22dx) Ic1 = I0 exp(-μ11dx -μ21dx) Figure 4 For a medium assumed to consist of four different types of materials, four measurements will allow enough information to obtain four equations with four unknowns. 4/8

13 Scintillator (transforms the X-ray energy into visible light, detected by a photo diode) Solid state semiconductor The gas detectors are less efficient than the other two types of detectors, but by using high pressure, and extended radial dimensions efficiencies as high as 40 % can be achieved. These deep detectors has the important property of being most sensitive to radially incoming X-rays thus providing inherence protection against too much scattered radiation. With the other two detectors, which are more like surface detectors, the scattered radiation cannot be separated, and must be removed by the mathematical reconstruction algorithm. This is possible, because the scattered radiation has little spatial structure, and can thus be detected and subtracted as a uniform blanket in the image matrix. With many detectors in each chain and many slices the total data sampling rate of a modern CT scanner is extremely high. At present, it is exactly this data sampling rate which limits the performance of state-of-the-art CT scanner technology. 2.3 Reconstruction The reconstruction of the slices from a large number of different projections forms an algebraic problem. This can be seen by considering a CT image with two by two pixels. If the object is irradiated with X-rays from two perpendicular directions, the detectors will measure the four values indicated in Figure 4. The four attenuation values of the CT image can now be found by solving four equations of four unknowns. The corresponding equations are: ln(i 0 /I r1 ) dx 1 = μ 11 + μ 12 (2) ln(i 0 /I r2 ) dx 1 = μ 21 + μ 22 (3) ln(i 0 /I c1 ) dx 1 = μ 11 + μ 21 (4) ln(i 0 /I c2 ) dx 1 = μ 12 + μ 22 (5) Note that the basic physics does not require sampling of projections for more than 180, as the measurement is basically a transmission measurement covering the entire depth forwards to backwards of For all projections, the measured values are added to all contributing pixels Figure 5 Back projection. Each attenuation value is put back into the cells of the image that are located at the line of sight. The same values are put into each cell. 5/8

14 Figure 6 Evolution of backprojection. The first five images are derived from filtered projections, whille the last is derived from raw projections. the object. However, because of system stability, artifact suppression and noise reduction, scans are normally acquired based on 360 acquisitions. However beautiful the algebraic reconstruction looks the practical application is difficult due to the larger number of equations and unknowns. Reconstructing a single slice represented by a 512 by 512 matrix corresponds to the diagonalization of such a matrix, which is no simple task. Some algorithms, however, obtain this goal by iterative measures: first making a guess of the distribution of attenuation values, subtracting the corresponding projections from the actual projections measured and then iteratively minimizing this error difference. 2.4 Filtered backprojection Because it is computationally more effective, the most used algorithm is the so-called filtered backprojection. Consider an image matrix whit pure zeros. Backprojection by itself simply fills the attenuation values of individual projections into each cell of the matrix along the line of sight. The values filled in, are added to those already in the image matrix. This is sought illustrated in Figure 5. When the backprojection is performed on a large number of projections, the final image begins to emerge, 6/8

15 Window width LL UL Greyscale value Window centerline Houndsfield units Figure 7 Windowing. Only HU between -300 and 600 are visualized in the gray scale bar. LL = lower level. UL = upper level (drawing not fully to scale). as seen in Figure 6. However, the image is blurred: a single point object with high attenuation (e.g. a thin tube of water in air) will by this reconstruction be depicted as a 1/r distribution. By filtering the measured projections before backprojection, this blurring can be reduced. The filtering is actually a convolution of the individual projection with a suitable spatial filter, amplifying high spatial frequencies and damping low spatial frequencies. The final reconstruction algorithm is often called LSFB, an abbreviation for linear superposition of filtered backprojections. The exact choice of filter function should be matched with the scanner characteristics, field of view and object of interest. There is no need to reconstruct with filters using higher spatial frequencies than the inherent limits given by the finite detector size in the detection chain. The reconstructed image represents the attenuation coefficients. These are re-calculated to Hounsfield units, and this image is displayed as gray values on the screen. However, the range of Hounsfields units (or attenuation) can be very large, and if only soft tissue is to be visualized, only a small window of values are displayed, as illustrated in Figure 7. Because of the large dymaic range of the CT scanner, it is often better from the beginning of the reconstruction to limit the interest area of the image values to a suitable range. For this reason reconstruction is often formed in brain window, lung window or bone window. 3 Example of clinical CT image Finally, a comparison between an anatomical photograph and a CT image from exactly the same plane is included in Figure 8. The data is from the Visible Human Project. From the CT image, it is very clear which types of tissue, that is best distinguished in the CT image. 4 Acknowledgements Student Jonas Henriksen is greatfully acknowledged for the help with the tables for Hounsfield values. 7/8

16 Figure 8 An anatomical photograph and corresponding CT image at a horizontal scan plane of the head. Data from: [1] 5 References [1] The visible human project: [2] Willi A. Kalender, "Computed Tomography", 2005, 2nd edition, Publicis Corporate Publishing, Erlangen. [3] Erich Krestel, "Imaging Systems for Medical Diagnostics", 1990, Siemens Aktiengesellschaft, Berlin and Munich. 8/8